The world is not enough

[red_ed]

TL;DR

Viewed from above, the world has 24 hours. But it doesn't add up.

Though experiment: imagine yourself floating above one of the poles of the earth. Since I'm in the Northern Hemisphere I will use the North pole. Looking down at Noon Greenwich time, the sun is directly above Greenwich.

Now freeze the tableau and imagine yourself as an infinitely fast runner, starting at Greenwich and running West, across oceans and cities and all that stuff. As you run you wil cross time-lines: 11am, 10am,...until you reach the terminator between today and yesterday, 12:01 am. One more step puts you into yesterday. Leave this imaginary observer in place and return a new observer to Greenwich.

Observer 2, starting at noon Greenwich, starts running East, crossing timelines: 1pm, 2pm...11:59pm. One more step and your observer crosses into tomorrow. He/she/it is also face-to-face with observer #1. Two observers. Three days (Yesterday, Today, Tomorrow) all at the same point.

It doesn't work. Yet we live it daily.

 

[red_ed]

You can add date-lines to the puzzle, but that simply complicates the puzzle without solving it.

 

[Dale]

Sorry, what is the puzzle that needs to be solved here?

 

[pinball1970]

TL;DR: Viewed from above, the world has 24 hours. But it doesn't add up.

Though experiment: imagine yourself floating above one of the poles of the earth. Since I'm in the Northern Hemisphere I will use the North pole. Looking down at Noon Greenwich time, the sun is directly above Greenwich.

Now freeze the tableau and imagine yourself as an infinitely fast runner, starting at Greenwich and running West, across oceans and cities and all that stuff. As you run you wil cross time-lines: 11am, 10am,...until you reach the terminator between today and yesterday, 12:01 am. One more step puts you into yesterday. Leave this imaginary observer in place and return a new observer to Greenwich.

Observer 2, starting at noon Greenwich, starts running East, crossing timelines: 1pm, 2pm...11:59pm. One more step and your observer crosses into tomorrow. He/she/it is also face-to-face with observer #1. Two observers. Three days (Yesterday, Today, Tomorrow) all at the same point.

It doesn't work. Yet we live it daily.

I don't see the issue. the earth makes one rotation every 24 hours, where we split today from yesterday is completely arbitrary. You can think of it when flying from West to east and back you gain and lose hours in those journeys, it is why we get jet lag because we are crossing the time zones.

 

[russ_watters]

It doesn't work. Yet we live it daily.

Just draw a polar view of Earth and label the time zones (or find one online) and you'll see it does work. The date line is what makes it work.

 

[Dale]

The date line is what makes it work.

Yes. Starting from Greenwich, one way you add 1 hour 12 times, then subtract 24 hours, then add 1 hour 12 more times. The other way you subtract 1 hour 12 times, then add 24 hours, then subtract 1 hour 12 more times.

 

[DaveC426913]

I will hazard what I think you may see as a paradox: Those two scenarios, when put tegether, create a single scenario: two observers, standing in the same place at the same time - each think it is a different day. One can literally face the other and say: "It's Tuesday." while the other insists "No, it's Monday". How can they both be correct?

Here is how you resolve the paradox:

We count Mondays and Tuesdays - and every other day of the week - by where the sun is - more relevantly, whether it has set and risen again.

Let's call our eastbound observer Evelyn and our westbound observer Wilbur.

Simply put: Evelyn has seen one more sunset/sunrise than Wilbur.

Evelyn's sunset and subsequent Tuesday arrived rather quickly, as she zoomed eastward, away from the sun. She actually watched it set in her rear view mirror. For her, all of Monday lasted maybe only 18 hours or whatever. She had a short nap in the brief dark, and it is now Tuesday morning.

Wilbur, on the other hand, chased the sunset; the sun has not dipped below his horizon at all. It is indeed, still Monday (albeit a long one) for him.

It's a real thing, not an illusion: They will spend the rest of their days with Wilbur having actually witnessed one more sunset than Evelyn.



Paradox resolved.

 

[A.T.]

You can add date-lines to the puzzle, but that simply complicates the puzzle without solving it.

Using time-zones without a date-line makes no sense. No wonder you are puzzled.

It doesn't work. Yet we live it daily.

You can use UTC if you don't like it.

 

[Ibix]

Isn't this, in fact, the happy ending to Jules Verne's Around the Word in Eighty Days? Fogg thinks he hasn't made it by one day because he forgot to reset his calendar when he crossed the dateline.

 

[DaveC426913]

Isn't this, in fact, the happy ending to Jules Verne's Around the Word in Eighty Days? Fogg thinks he hasn't made it by one day because he forgot to reset his calendar when he crossed the dateline.

[EDITED per @A.T.'s comment, below]
[EDITED per @kuruman's comment, below]

And, leaving out all the math, one can choose to look at it intuitively: recording subjective sunsets in his log, he literally recorded 81 instead of 80.

By transiting the Earth once, Eastward, he saw one more sunset than every one else. Thus he thought it was one day later than for those back at the club.

 

[A.T.]

By transiting the Earth once, Eastward, he saw one less sunset than every one else. Thus it is, for him, one day earlier.

No. By transiting the Earth once, eastward, he saw one more sunset than everyone else. That's why he intially assumed that he arrived too late.

 

[kuruman]

I will hazard what I think you may see as a paradox: Those two scenarios, when put tegether, create a single scenario wherein two observers, standing in the same place at the same time - each think it is a different day. One can literally face the other and say: "It's Tuesday." while the other insists "No, it's Monday".

Several years ago I took a direct flight from Dallas to Beijing. Here is a relevant excerpt from the notes I kept during the trip.

The International Date Line (IDL) runs between the North American and Asian shores through​

the Bering Strait. I watched “local time” displayed on the flight information monitor to see what would happen when we crossed the IDL. It changed discontinuously from 15:32 to 10:32 of the next day. I imagined two people separated by a few feet on either side of the line right below the plane. The Asian is 19 hours ahead of the North American. They both agree on the duration of daylight, but they disagree on the sunrise and sunset times and the date.​

To @red_ed:
This is like two people facing each other on a conventional unit circle on either side of the positive x-axis. The person slightly above the axis says, "I am at angle 0°" while the person slightly below the axis says, "I am at angle 360°."

As others have said local time is a convention that is specific to each point on the Earth and attached to it. Have you wondered "what time it is" on the International Space Station that goes around the Earth about 16 times a day?

 

[DaveC426913]

No. By transiting the Earth once, eastward, he saw one more sunset than everyone else. That's why he intially assumed that he arrived too late.

Derp. Fixed.

 

[Nugatory]

They will spend the rest of their days with Wilbur having actually witnessed one more sunset than Evelyn.

There is a (possibly apocryphal) account of great consternation when Magellan returned to Spain and his ship’s log was missing a day….

 

[A.T.]

As others have said local time is a convention

And we could in principle get rid of it, and instead get used to the same hour on a clock meaning different phases of the day-night cycle in different places on Earth.

Just like the same month means a different season on the two hemispheres.

 

[russ_watters]

There is a (possibly apocryphal) account of great consternation when Magellan returned to Spain and his ship’s log was missing a day….

Something I didn't learn in school (or maybe just misremembered) is that Magellan did not return to Spain, he was killed in the Philippines. The circumnavigation was completed by Captain Juan Sebastian Elcano. Weird it is still credited to Magellan.

https://en.wikipedia.org/wiki/Ferdinand_Magellan

 

[kuruman]

And, leaving out all the math, one can choose to look at it intuitively: recording subjective sunsets in his log, he literally recorded 89 instead of 88.

So why is the title of the book "Around the World in 80 Days"?

 

[red_ed]

Wow. I am amazed by the response.

```
I will hazard what I think you may see as a paradox: Those two scenarios, when put tegether, create a single scenario wherein two observers, standing in the same place at the same time - each think it is a different day. One can literally face the other and say: "It's Tuesday." while the other insists "No, it's Monday".
```

Nope. Exactly the opposite. The two entities, one which travelled East, the other West, face each other across the 12pm line. Each knows they are in the same day since they both started at noon in Greenwich and travelled within the same day up to the midnight line. And each knows one more step will put them into the next (or previous) day.

And both are right.

It is impossible. Yet we live it every day.

 

[Ibix]

It is impossible.

I assume you didn't actually read the responses. It is only inconsistent if (as you have done) you ignore the International date line. That's why we have it, and why we don't ignore it.

 

[DaveC426913]

So why is the title of the book "Around the World in 80 Days"?

Ohmygod double derp. Somebody take my keyboard away from me.

 

[russ_watters]

[Sigh] Not sure if this is an exceptionally low effort OP or a crank-yanker, but just to move this along:

 

[Ibix]

[Sigh] Not sure if this is an exceptionally low effort OP or a crank-yanker, but just to move this along:

View attachment 369505

Note: the "night" and "day" there is conventional. The actual areas of light and dark aren't shown.

 

[Dale]

Nope. Exactly the opposite. The two entities, one which travelled East, the other West, face each other across the 12pm line. Each knows they are in the same day since they both started at noon in Greenwich and travelled within the same day up to the midnight line. And each knows one more step will put them into the next (or previous) day.

The international date line fixes exactly that.

 

[PeroK]

Wow. I am amazed by the response.

```
I will hazard what I think you may see as a paradox: Those two scenarios, when put tegether, create a single scenario wherein two observers, standing in the same place at the same time - each think it is a different day. One can literally face the other and say: "It's Tuesday." while the other insists "No, it's Monday".
```

Nope. Exactly the opposite. The two entities, one which travelled East, the other West, face each other across the 12pm line. Each knows they are in the same day since they both started at noon in Greenwich and travelled within the same day up to the midnight line. And each knows one more step will put them into the next (or previous) day.

And both are right.

It is impossible. Yet we live it every day.

Are you a flat Earther?

 

[DaveC426913]

I would ask that the OP put their cards on the table and state what the intent of this thread is.

None of us have a problem with timezones and the international date line. The OP hints that they might have a problem with it, even while saying "yet we live with it". We can't properly answer a question you have not yet asked.

So what exactly is the problem? I ask @red_ed to state it and, if they can't, I ask that the thread be locked until/unless the problem can be properly defined.

 

[.Scott]

Hello @red_ed :

As you travel from Greenwich eastward around the globe, your time will jump in this sequence +1hr, +1hr, +1hr, +1hr, +1hr, +1hr, +1hr, +1hr, +1hr, +1hr, +1hr, -23hr, +1hr, +1hr, +1hr, +1hr, +1hr, +1hr, +1hr, +1hr, +1hr, +1hr, +1hr, +1hr. And you can work out the increments in a westward trek.

Since the date line only gives you a 23-hour transition (not a 24-hour transition), there will be a 1-hour period every day when your two observers reach the date line on the same calendar date. And that 1-hour period starts at noon Greenwich time (the moment you picked for your experiment).

The two entities, one which travelled East, the other West, face each other across the 12pm line. Each knows they are in the same day since they both started at noon in Greenwich and travelled within the same day up to the midnight line. And each knows one more step will put them into the next (or previous) day.

And both are right.

It is impossible. Yet we live it every day.

Both are wrong - and will remain wrong until 1UTC.

 

[russ_watters]

So what exactly is the problem? I ask @red_ed to state it and, if they can't, I ask that the thread be locked until/unless the problem can be properly defined.

It's getting there, yes.

 

[.Scott]

It's getting there, yes.

I believe I have provided the answer that the Op was seeking. It was just a puzzle that was ineffectively presented.

 

[Baluncore]

The sum of my net global travel, has me travelling 1½ laps of the Earth from West to East.

Should I make my next circumnavigation from East to West, to undo the extra day-night cycle of aging that I have suffered?

Am I celebrating my birthday one, or two, days early?

 

[.Scott]

The sum of my net global travel, has me travelling 1½ laps of the Earth from West to East.

Should I make my next circumnavigation from East to West, to undo the extra day-night cycle of aging that I have suffered?

Am I celebrating my birthday one, or two, days early?

I have crossed the dateline 6 times - three in each direction, so I am "evened out". On two of the return trips, the days progressed Friday, Saturday, Sunday, Saturday, Sunday, Monday. So I am two weekends up on life. Also, I once had three vernal equinoxes in a row before finally having another autumnal equinox.